Abstract

The arithmetic theta function is a modular form of weight 3/2 valued in the arithmetic Chow group of the arithmetic surface attached to a Shimura curve of Q.  This function can be used to define a theta lift from modular forms of weight 3/2 to the elements of the arithmetic Chow group.  A conjectural analogue of a result of Waldspurger gives a characterization of the nonvanishing of this arithmetic theta lift in terms of (i) local obstructions and (ii) the nonvanishishing of the central derivative of the L-function.  This result is proved in some cases.